Does DokuWiki have to Run on GNU/Linux?

The system requirements don't mention what Operating System you're supposed to run on your server. Can I only run this wiki on GNU/Linux?

No, it only needs a web server and PHP. Whatever OS supports those is usually fine. Please see OS-specific installation instructions for a variety of OS. (The list is not exhaustive. If your OS is not listed there, it might well run DokuWiki anyway.)